At best, sentence a) can be interpreted as one with redundance. It is an infeliticious mix between these two (acceptable) sentences:

"Just because you're a woman, you're not overly sensitive,"and"(The fact) that you're a woman doesn't mean that you're overly sensitive."

In a normal sentence, what comes before "...doesn't mean that..." is the SUBJECT of the sentence, as in:"This (SUBJECT, (pronoun)) doesn't mean that you're stupid".In somewhat simplified terms, the subject of an acceptable English sentence should be a nominal element, i.e. a noun, a pronoun, or a nominal subordinate clause ("that"-clause):

"(Just) because you're a woman" is an adverbial clause, and these cannot funcion as subjects of sentences in English, hence the unacceptability of the following sentence:

*"Because I found the money (*SUBJECT, (adverbial subordinate clause)), is very nice"

So, the sentence: *"Just because you're a woman (*SUBJECT, (adverbial subordinate clause)) doesn't mean that you're overly sensitive", where a clause that refers to a causal state of affairs poses as the subject, is unacceptable.

What, then, of the following two varieties of the sentence in question?:

b) "Just because you're a woman, it doesn't mean that you're overly sensitive,"andc) "Just because you're a woman, that doesn't mean that you're overly sensitive."

These two sentences don't sound quite as bad as sentence a), at least not in my ears, but are they well-formed?They differ from the first one in that, in both cases, the main (superordinate) clause has a subject ("it" and "that" respectively), so we are not forced to interpret the adverbial clause as the subject of the sentence.

However, the sentences, like sentence a), seem to be an amalgamation of two different, individually acceptable sentences:

"Just because you're a woman you're not overly sensitive"and"You're a woman, but it/that doesn'tmean that you're overly sensitive."

We can question the acceptability of sentences b) and c) based on our intuition, if we try a question/answer excercise:

I would further argue that sentences b) and c) are unacceptable because the pronouns that function as the subjects of the sentences have anaphoric reference (they refer to something in the preceding linguistic context), and what they refer to is a causal construction ("Just because you're a woman"), and, again, this is not a "semantic role" typically fulfilled by the subject of a sentence.

Surprisingly enough, I hear all three varieties expressed regularly, also among people that otherwise seem to be quite eloquent.